Question

The pair of points is on the graph of an inverse variation. find the missing value. (5,4) and (x,7)

Answer 1

One form of the relation of inverse variation is y = k/x.

first step:  Find the value of k:    Taking the values x=5 and y = 4, 4=k/5, or k=20.  Then,   y = 20/x.

Next:  Let y = 7 and find the corresp. value of x:  7=20/x, or 7x=20, or

x = 20/7    (answer) 

Answer 2

To the risk of sounding redundant.

$\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf (5,4)\textit{ we also know that } \begin{cases} x=5\\ y=4 \end{cases}\implies 4=\cfrac{k}{5}\implies 20=k \\\\\\ therefore\qquad \boxed{y=\cfrac{20}{x}} \\\\\\ (x,7)\textit{ when y = 7, what is \underline{x}?}\qquad 7=\cfrac{20}{x}\implies x=\cfrac{20}{7}\implies x=2\frac{6}{7}$